Multi-Factorial Complex Effects Analysis of Energy Consumption Time Series with the Novel Nonlinear Grey Interaction Model

Objective and accurate estimation of energy consumption in the industrial sector is essential to formulate energy conservation and achieve sustainable development. Due to the nonlinear relationships, the interaction effect among influencing factors and improvement of parameter estimation are rarely considered together in energy consumption analysis. To address these issues, the nonlinear grey fuzzy integral model (NFLGM (1, N) model) is developed for energy consumption analysis. Firstly, the Choquet fuzzy integral is introduced to reflect the interaction effect; the power exponential term and the random term are introduced to represent the nonlinear effect and the random trend. Secondly, a novel hybrid parameter optimization algorithm is designed to improve the model precision. The model’s structural parameters are estimated by using the Least Squares Support Vector Machine and complex effect parameters using a two-stage optimization model. Finally, 30 years of energy consumption data are selected for computational experiments. NFLGM (1, N) model consistently exhibits higher stability and accuracy. The computational results indicate that energy consumption in the United States is expected to increase by 0.31% from 2020 and decrease by 3.58% (China) and 3.87% (Japan). These findings enable the identification and quantification of the complex effects of energy consumption systems and provide actionable recommendations for decision-makers.